Related papers: Partitioning the Sample Space for a More Precise S…
The fractional order generalization of Shannon entropy proposed by Ubriaco has been studied for discrete distributions. In the current paper, we conduct a detailed study of the continuous analogue of this entropy termed as fractional…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical…
In this work we determine and discuss the entropic uncertainty measures of Shannon type for all the discrete stationary states of the multidimensional harmonic systems directly in terms of the states' hyperquantum numbers, the…
The mutual information (MI) between two random variables is an important correlation measure in data analysis. The Shannon entropy of a joint probability distribution is the variable part under fixed marginals. We aim to minimize and…
The Shannon entropy is used as a basis for applying different lemmas and conjectures concerning the set of gaps between prime numbers G_p , thus estimating several measures of it. The same procedures are applied to artificially created…
We consider the problem of estimating Shannon's entropy $H$ from discrete data, in cases where the number of possible symbols is unknown or even countably infinite. The Pitman-Yor process, a generalization of Dirichlet process, provides a…
The Shannon entropy is a widely used summary statistic, for example, network traffic measurement, anomaly detection, neural computations, spike trains, etc. This study focuses on estimating Shannon entropy of data streams. It is known that…
This paper investigates what can be inferred about an arbitrary continuous probability distribution from a finite sample of $N$ observations drawn from it. The central finding is that the $N$ sorted sample points partition the real line…
We present a numerical study of the application of the Shannon entropy technique to the planar restricted three-body problem in the vicinity of first-order interior mean-motion resonances with the perturber. We estimate the diffusion…
We introduce a method for quantifying the inherent unpredictability of a continuous-valued time series via an extension of the differential Shannon entropy rate. Our extension, the specific entropy rate, quantifies the amount of predictive…
Information has an entropic character which can be analyzed within the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is…
We show that a newly proposed Shannon-like entropic measure of shape complexity applicable to spatially-localized or periodic mathematical functions known as configurational entropy (CE) can be used as a predictor of spontaneous decay rates…
This paper proposes a novel entropy encoding technique for lossless data compression. Representing a message string by its lexicographic index in the permutations of its symbols results in a compressed version matching Shannon entropy of…
The entropic uncertainty measures of the multidimensional hydrogenic states quantify the multiple facets of the spatial delocalization of the electronic probability density of the system. The Shannon entropy is the most adequate uncertainty…
The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools…
We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…
Compressed Counting (CC) [22] was recently proposed for estimating the ath frequency moments of data streams, where 0 < a <= 2. CC can be used for estimating Shannon entropy, which can be approximated by certain functions of the ath…